02. Hypothesis testing

02. Hypothesis testing - Hypothesis testing Terminology •...

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Unformatted text preview: Hypothesis testing Terminology • Null hypothesis – e.g. H0: µ = 1 0 , H0: p = .5 , H0: µ1 = µ2 • Alternative hypothesis – e.g. H1 : µ ≠ 1 0 , H1: p < .5 , H1 : µ1 > µ2 • • • • • • Type I error? Type II error? Significance Level? Critical Region? p-value? Power? 2 Type I and II errors • Type I error – Reject H0 when H0 is true • Type II error – Accept H0 when H0 is false • Probabilities of Type I and II errors should be as small as possible – Fixed sample size • reducing probability of type I error ->increases probability of type II error 3 Hypothesis testing approach – significance level • FIX the maximum allowable probability of Type I error = α, significance level of the test • Test is then arranged to minimize Type II error • Most expensive error should represent Type I error • Type I error can be fixed • Under more control than type II error 4 Hypothesis testing example • Large sample size σ x ~ N (µ , ) n 2 • One sided test – H0:µ = µ0 vs H1:µ > µ0 – e.g. H0:µ = 1 0 vs H1:µ > 1 0 I I I I I I is true σ2 n α µ0 Critical region: Reject H0 µ0 + k x Hypothesis testing approach – significance level • FIX the maximum allowable probability of Type I error = α, significance level of the test • Reject H0 if test statistic lies in the critical region x − µ0 > zα 1 σ n 7 Computer Output (p-value) • p-value is a measure of exactly where the test-statistic lies in the critical region – Smaller p-value -> more significant result • Reject H0 if p-value is less than α p-value measures how significant a result is p-value µ0 x Hypothesis testing approach – power • Standard tests are designed to minimize probability of Type II error = β • Power of the test = 1 – β • Standard test designed to have maximum possible power (depending on effect size) • Recommended power ∼ 0.8 • Fixed n - increase power by relaxing α? • 10 ...
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02. Hypothesis testing - Hypothesis testing Terminology •...

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